Given two integers β and p as well as β graph classes
H1β,β¦,Hββ, the problems
GraphPart(H1β,β¦,Hββ,p),
VertPart(H1β,β¦,Hββ), and
EdgePart(H1β,β¦,Hββ) ask, given graph
G as input, whether V(G), V(G), E(G) respectively can be partitioned
into β sets S1β,β¦,Sββ such that, for each i between 1 and
β, G[Viβ]βHiβ, G[Viβ]βHiβ, (V(G),Siβ)βHiβ respectively. Moreover in GraphPart(H1β,β¦,Hββ,p), we request that the number of edges with
endpoints in different sets of the partition is bounded by p. We show that if
there exist dynamic programming tree-decomposition-based algorithms for
recognizing the graph classes Hiβ, for each i, then we can
constructively create a dynamic programming tree-decomposition-based algorithms
for GraphPart(H1β,β¦,Hββ,p),
VertPart(H1β,β¦,Hββ), and
EdgePart(H1β,β¦,Hββ). We show that, in
some known cases, the obtained running times are comparable to those of the
best know algorithms